Angle Insensitive Color Filters in Transmission Covering the Visible Region

Angle insensitive color filter based on Metal-SiOx-Metal structure is proposed in this paper, which can keep the same perceived transmitted color when the incidence angle changes from 0° to 60°, especially for p-polarization light. Various silicon oxide films deposited by reaction magnetron sputtering with a tunable refractive index from 1.97 to 3.84 is introduced to meet the strict angle insensitive resonance conditions. The angle resolved spectral filtering for both p-polarization light and s-polarization light are quite well, which can be attributed to the different physical origins for the high angular tolerance for two polarizations. Finally, the effect of SiOx absorption and Ag thickness on the peak transmittance are analyzed.

The lossless Drude model (ε 2 = 1 − ω p 2 /ω 2 , where ω p is the bulk plasma frequency of the metal) is adopted to describe the dielectric function of the metallic layers. Both metal and dielectric are presumed nonmagnetic (μ 1 = μ 2 = 1). It can be seen from Fig. 2(a) that the light propagating in the MDM structure has three modes: radiative mode, quasi-bound mode and propagating surface plasmon polariton (SPP) mode from top to bottom. Here we mainly focus on the quasi-bound mode. When the parallel part of the wave vector κ approaches infinity, ω (κ ) (the dispersion frequency as a function of κ ) tends towards ω sp , which is the surface plasmon frequency at the metal-spacer interface. At this frequency, the optical constant of metal is equal in magnitude and opposite in sign to that of the dielectric: In this case, with the proper thickness of the dielectric layer λ ε = ( ) d 4 2 dielectric sp dielectric the frequency at κ = 0 will coincide with ω sp , (λ sp = 2π c/ω sp is the free-space surface plasmon wavelength) then the dispersion band of quasi-bound mode may become almost completely flat. Therefore, such a flat dispersion band indicates that the resonance occurs approximately at the same wavelength for all incidence angles. The angular insensitive phenomenon of this structure for p-polarization can also be explained by Fabry-Perot resonant cavity theory. As shown in Fig. 2(b) the round-trip phase shift in the MDM structure includes two parts: the propagation phase shift accumulated when the light wave goes through the dielectric region and the reflection phase shift at the metal-dielectric interfaces. If Equation (1) and (2) are satisfied, the aggregate reflection phase shift at the metal-spacer interfaces almost exactly cancels the phase shift due to the propagation of the wave in the  direction perpendicular to the interfaces in the spacer region and the total phase shift reaches approximately 2π for all incident angles 12,15 .
As known to us, Ag is a good conductive metal and the real part of its refractive index is quite small at visible region. So the relative permittivity of Ag is approximately described as ε Ag = − κ Ag 2 , κ Ag is the imaginary part of refractive index of Ag. For a typical dielectric material, the imaginary part of their refractive index is close to 0, leading to ε dielectric = n 2 . Therefore, to achieve the angle insensitive properties for p-polarized light, the refractive index of the dielectric material should be equal to κ Ag . At visible region, Ag presents anomalous dispersion properties. As shown in Fig. 3(a), the extinction coefficient of Ag increases monotonously from 1.9 to 4.5 as the wavelength increases from 400 nm to 700 nm. According to n = κ Ag , dielectric layers with the matching refractive index are necessary to fabricate the angle insensitive MDM filters. Unfortunately, the refractive index of dielectric material commonly used in the visible region for optical coatings is limited to 2.5. Thus, only filters with resonant wavelength less than 480 nm were fabricated, e.g., ZnS(n = 2.5) at the resonant wavelength of 474 nm for transmission type and SiO 2 (n = 1.46) at the resonant wavelength of 352nm for reflection type 12,15 .
Silicon as a semiconductor material is widely used to manufacture the mid-infrared optical filters. It has a high refractive index (n > 4.5) in visible region which is a good candidate to construct the angle insensitive MDM filter with Ag. Moreover, SiO x film can be achieved if oxygen gas is introduced during the deposition process of silicon. The refractive index of SiO x determined by the composition of the material (the oxygen content in the SiO x film) can be continuously tuned by controlling the deposition parameters. Theoretically, SiO x can turn into pure amorphous silicon with no oxygen or silicon dioxide with sufficient oxygen as the critical case 16,17 . Therefore, the angle insensitive filters at various resonant wavelengths over the whole visible region can be obtained.
Reactive magnetron sputtering is used to deposit the SiO x films in our study. The silicon with the purity 99.999% is the target. The substrate is a double polished fused silica with 15 × 15 mm and the substrate is kept at room temperature during the deposition. The distance between the target and substrate is 15cm. The chamber is pumped to a base vacuum pressure 5 × 10 −5 Pa. Argon and Oxygen are introduced respectively as the sputtering and reactive gas. The technical parameters including the sputtering power, the deposition vacuum pressure and the oxygen flow rate will affect the optical properties. Among these parameters, oxygen flow rate has a largest impact on the optical constant of the SiO x film. Thus, the SiO x film with different refractive index was fabricated by tuning the oxygen/ argon flow rate ratio. The Ar flow rate is set at 90 sccm, the deposition pressure is 2 × 10 −2 Pa and the sputtering power is kept at 400 w.
The optical constants of the SiO x film shown in Fig. 3(a), were determined by the photometry method by fitting the measured reflectance and transmittance curves. The detailed fitting method and fitting qualityare provided in the supplementary information. The refractive index of SiO x in the visible region is gradually reduced as the O2 flow rate is increased. The refractive index@550 nm reduces from 4.2 to1.7 when the O2 flow rate changes from 0 sccm to 3 sccm. The composition of the films characterized by XPS(X-ray photoelectron spectroscopy) is shown in Fig. 3(b). As O2 flow rate is increased, the content of oxygen in SiO x film is raised up owing to the reaction between Si and O2 during the sputtering deposition. For comparison, the extinction coefficient of Ag is also plotted in Fig. 3(a). According to the resonance condition, κ Ag = n SiOx can be deduced from Equation (1) if the extinction coefficient of SiO x film is ignored. It implies that the intersection between the Ag extinction coefficient curve and the SiO x index curve indicate a perfect resonance at the selected wavelengths. Therefore, the green dots marked in Fig. 3 are the ideal resonant points. To construct an insensitive color filter at a specific central wavelength, a SiO x film with a specific oxygen content and refractive index is required. By adjusting the oxygen flow rate during the deposition, the refractive index of SiO x films can be varied from 1.46 to 4.2. So, the resonance condition will be satisfied with tunable SiO x film covering the whole visible light region and various colors can be obtained with this method as desired. In our study, five color filters with different central wavelengths as indicated in Fig. 3(a) are experimentally manufactured. The corresponding refractive index, thickness and oxygen flow rate during the deposition of SiO x layer at the given resonance wavelengths are listed in Table 1.
For the transmission filters, the absorption caused by the spacer layer must be considered. As is shown in Fig. 3(b), all the SiO x films show a normal dispersion in the visible region. The extinction coefficient of different SiO x fims decreases as the content of oxygen in the film increases, i.e., a lower refractive index of the SiO x film leads to a lower absorption. For the selected central wavelengths of the angle insensitive filters shown as the green dots in Fig. 3, the extinction coefficient of the corresponding SiO x film decreases as the central wavelength turns shorter. Thus, the filter with a shorter central wavelength will have a relative higher peak transmittance.
The angle resolved transmission spectra of these devices calculated by transfer matrix method as well as the measured results are shown in Fig. 4(a-c) for p-polarization 6 . The angle resolved transmittance of these devices were measured by the spectrophotometer (Shimadzu UV-3101PC) with a rotating sample stage. For p-polarization light, it is obvious that good angle insensitivity is remained for all these fabricated filters up to 60 degrees, matching well with the simulation results and confirming the theoretical analysis. Generally, the optical property of these color devices for s-polarization must be taken into account as well for its practical application. Figure 4(d-f) show the simulated and measured angle resolved transmission of these devices for s-polarization. It is not hard to find that the angle insensitive property for s-polarization is not bad, which could be ascribed to the high refractive index of SiO x 10 . When the incidence angle in air increases to 60°, the refraction angle in SiO x layer is still small, which leads to a small resonance shift. The small difference of the resonant wavelengths between the simulated and the measured are caused by the errors of the sputtering conditions and the thickness of Ag layers. For the fabricated devices the peak transmittance for both two polarizations decreases as the resonant wavelength goes towards long wavelength, this is because the corresponding extinction coefficient of SiO x is increased, which can be seen in Fig. 3(b). The peak transmittance reaches a stable level of 30% as the resonant wavelength increases. This is because when the extinction coefficient increases, the refractive index increases as well. According to Equation (2), the physical thickness of SiO x films with longer resonance wavelength are thinner than that of films with shorter resonance wavelength, which is shown in Table 1. Therefore, the total absorption caused by SiO x films can be restrained and be kept at an acceptable level. While the incidence angle increases, the peak transmittance of p-polarization light will be increased and the s-polarization light decreased, thus leads to a constancy for the average transmittance, shown in Fig. 5. For unpolarized incidence, the peak transmittance of all these filters is higher than 32%, which provides a guarantee for the practical applications of this transmission filters. And the half-band width (about 100 nm) is relatively wide for the thin Ag layers which could not provide enough reflectance but the peak transmittance and the half-band width must be balanced. So the MDM angle insensitive filters with tunable SiO x is available for non-polarized case and can be potentially applied for diverse colorful applications. In order to demonstrate the color change quantitatively, the spectral data of average transmittance are transformed into CIEDE2000 Color-Difference Chart and are shown in Table 2. It can be seen that the color change is not large for all the five filters.
It is worth mentioning that the thickness of the Ag layer carries a huge impact on the optical properties of the proposed filters, which influences not only the peak transmittance of the filters, but also the angle insensitive characteristics and the resonant wavelengths. When the Ag layers are thick enough (at least 30 nm), perfect angle insensitive characteristics (less than 5 nm resonant wavelength shift at the incidence angle of 60°) will be obtained, especially for p-polarization, however the peak transmittance will be decreased to less than 10% at red spectral band. When the thickness of the Ag layers decreases, the peak transmittance will be increased greatly but the filters will have a decline in angle insensitive properties and the center resonant wavelengths will have a red shift compared with the designed position. Therefore, thickness of 16 nm is selected for the Ag layers balance the peak transmittance and the angle insensitive characteristic.  Figure 6 is a photo image of the fabricated devices taken with outdoor ambient light under sunshine at four different angles up to 45°. The back ground is clearly seen through the devices owing to the relatively high peak transmittance and when the devices are rotated from 0° to about 45°, both the transmittance and the color change   Table 1 and Fig. 6. very little. Hence, the proposed devices are fabricated only through vacuum deposition and well performed can have enormous potential in applications where angle insensitive characteristic are needed.

Discussion
In conclusion, a compact film structure based on MDM resonator is proposed to achieve the efficient angle insensitive color filtering for transmission spectrum across the whole visible light wavelengths. Silicon oxide deposited by reaction magnetron sputtering with a tunable refractive index is introduced to meet the strict rigorous conditions demands of the materials. Color filters fabricated in our study can present the same perceived color up to 60 degrees with the peak transmittance of over 32%, which agrees well with the simulation results. The angle resolved spectral filtering for p-polarization light is as well as that for s-polarization, which can be attributed to the different physical origins for the high angular tolerance for two polarizations. Moreover, the transmittance can be optimized by controlling the thickness of Ag layers. Furthermore, gold can be adopted in such structure for the infrared region. The method has enormous potential in applications of display, remote sensing, decoration, and anti-counterfeiting.    Methods Simulation. Simulation of the transmittance of the fabricated filters was performed by the transfer matrix method. In our simulation, the optical constants of Ag was from the data of Palik 18 and the refractive indexes, extinction coefficient and thickness of SiO x were experimentally determined by spectrometry method considering both the reflectance and the transmittance curves. The details are provided in the supplementary information.
Device fabrication. The proposed color filters were manufactured on a double polished fused silica with 15 × 15 mm. The film stacks were all deposited by magnetron sputtering with the base vacuum pressure better than 5 × 10 −5 Pa. During the deposition, the substrates were kept at room temperature. The distance between the target and substrate is 15cm. For SiO x , the Ar flow rate is set at 90sccm, the deposition pressure is 2 × 10 −2 Pa and the sputtering power is kept at 400w. For Ag the Ar flow rate is set at 40sccm , the deposition pressure is 1.5 × 10 −1 Pa and the sputtering power is kept at 70 w.
Optical characterization. The reflectance/transmittance measurement was performed by the spectrophotometer (Shimadzu UV-3101PC).